Where a function of several variables is given numerically in tabular form, an orthonormalization technique allows an approximation of the numerical data to be determined in a convenient functional form. In this technique, the speed and accuracy of coefficient computation are much improved

Ingram, H. L.

English

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December 1966	 Brief 66-10579 
NASA TECH BRIEF	
I& 
NASA Tech Briefs are issued to summarize specific innovations derived from the U.S. space program, 
to encourage their commercial application. Copies are available to the public at 15 cents each 
from the Clearinghouse for Federal Scientific and Technical Information, Springfield, Virginia 22151. 
An Orthonormalization Procedure. for Multivariable Function Approximation 
The problem: 
In many types of scientific and engineering prob-
lems, a table of two or more columns of data occurs 
and it is often desirable to present this data in a more 
useful form. The usual methods for performing this 
task are the many different techniques of multivari-
able function approximation such as the least squares 
procedures that require appreciable time to compute 
the coefficients. 
The solution: 
Where a function of several variables is given 
numerically in tabular form, an orthonormalization 
technique allows an approximation of the numerical 
data to be determined in a convenient functional 
form. The method requires much less computational 
work than the usual least squares technique, and
allows more easily controlled accuracy. In this tech-
nique, the speed and accuracy of coefficient compu-
tation are much improved. Additionally, a very clear 
and useful physical interpretation of the procedure is 
available to aid in the choice of terms to be included in 
the approximating formulas. 
Note: 
Inquiries concerning this innovation may be di-
rected to:
Technology Utilization Officer 
Marshall Space Flight Center 
Huntsville, Alabama 35812 
Reference: B66-10579 
Patent status: 
No patent action is contemplated by NASA. 
Source: Hugo L. Ingram 
(M-FS- 1313) 
Category 01 
This document was prepared under the sponsorship of the National 
Aeronautics and Space Administration. Neither the United States 
Government nor any person acting on behalf of the United States
Government assumes any liability resulting from the use of the 
information contained in this document, or warrants that such use 
will be free from privately owned rights.
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An orthonormalization procedure for multivariable function approximation

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